Question
Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.
Solution
Any positive number, which has more than two factors, is called a composite number.
Since,
7 × 11 × 13 + 13 = 13 × (7 × 11 + 1)
= 13 × 78
= 13 × 13 × 3 × 2
that is, the given number has more than two factors and it is a composite number.
Similarly,
7 × 6 × 5 × 4 × 3 + 5
= 5 × (7 × 6 × 4 × 3 + 1)
= 5 × 505
= 5 × 5 × 101
⇒ The given number is a composite number.
